Question about using FOIL method

Question

Problem:  (3√3 + 3√27)(2√3-√27)

 

In my textbook it says to first put "like radicals together" so I started with setting up this problem as:

(3√3 + 2√3)(3√27-√27)

 

However, in the problem explanation it uses the FOIL method. Why did it not put "like radicals" together instead of the FOIL method? When do you know when to put "like-radicals" together and when to use the FOIL method?

 

Thanks!

Answer 1

Gab, your two binomials are each factors, so you can't just swap out terms from one to the other. Remember back to (2x + 5)(x - 3). You didn't swap out and make it (2x + x)(5 - 3). If you are simply adding and subtracting, you group like radicals. Because you are multiplying, you do not!

Answer 2

Never heard of the "like radicals" method. Not sure how, if, it works

I would stick with FOIL

 

Checking

(3√3 + 3√27)(2√3-√27)

(6)(3) + 6√81 - 3√81 - (3)(27)   That's FOIL

18 + 72 - 27 - 81

-18

 

(3√3 + 2√3)(3√27-√27)     "like radicals"

(9)(9) + 6√81 - 3√81 - 2√81

81 + 54 - 27 - 18

90

 

Don't think so. I'd stick with FOIL.